Pseudopotentials, Lax Pairs and Bäcklund Transformations for Generalized Fifth-Order KdV Equation

2011 ◽  
Vol 55 (1) ◽  
pp. 25-28 ◽  
Author(s):  
Yun-Qing Yang ◽  
Yong Chen
Keyword(s):  
Kdv Equation ◽  
Bäcklund Transformations ◽  
Lax Pairs ◽  
Backlund Transformations ◽  
Fifth Order

scholarly journals Bäcklund Transformations between the KdV Equation and a New Nonlinear Evolution Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Xifang Cao
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
The Other ◽  
Bäcklund Transformations ◽  
Backlund Transformations ◽  
The Kdv Equation ◽  
New Equation

We first give a Bäcklund transformation from the KdV equation to a new nonlinear evolution equation. We then derive two Bäcklund transformations with two pseudopotentials, one of which is from the KdV equation to the new equation and the other from the new equation to itself. As applications, by applying our Bäcklund transformations to known solutions, we construct some novel solutions to the new equation.

scholarly journals Bäcklund transformations for several cases of a type of generalized KdV equation

2004 ◽  
Vol 2004 (63) ◽  
pp. 3369-3377
Author(s):  
Paul Bracken
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
Bäcklund Transformations ◽  
Backlund Transformation ◽  
Generalized Kdv Equation ◽  
Backlund Transformations ◽  
De Vries ◽  
Derivative Term

An alternate generalized Korteweg-de Vries system is studied here. A procedure for generating solutions is given. A theorem is presented, which is subsequently applied to this equation to obtain a type of Bäcklund transformation for several specific cases of the power of the derivative term appearing in the equation. In the process, several interesting, new, ordinary, differential equations are generated and studied.

BÄCKLUND TRANSFORMATIONS AND LAX PAIRS FOR THE NONLINEAR KLEIN–GORDON EQUATION WITH SYMBOLIC COMPUTATION

2009 ◽  
Vol 23 (11) ◽  
pp. 2511-2521
Author(s):  
XIAO-GE XU ◽  
YI-TIAN GAO ◽  
GUANG-MEI WEI
Keyword(s):  
Symbolic Computation ◽  
Gordon Equation ◽  
Bäcklund Transformations ◽  
Sine Gordon Equation ◽  
Lax Pairs ◽  
Special Cases ◽  
Backlund Transformations ◽  
Klein Gordon ◽  
Pulse Waves ◽  
Klein Gordon Equation

In this paper, the nonlinear Klein–Gordon equation describing the propagation of pulse waves in plasma or waveguide is investigated. With symbolic computation, the generalized Bäcklund Transformations (BTs) for this equation are constructed under different conditions. It is shown that the BTs published in the previous literature for the Sine–Gordon equation, Sinh–Gordon equation, and Liouville equation all turn out to be special cases of the results in the present paper. Moreover, the corresponding Lax pairs are explicitly derived from the obtained BTs through some transformations.

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